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Underground Temperature

THE Underground Temperature Committee of the British Association have presented a summary (drawn up by Professor Everett) of the results contained in all their reports (fifteen in number) up to the present date, of which the following is an abridgment: The results are classified under the heads: A. Instruments. B. Methods of observation. C. Questions affecting correctness of observations. D. Questions affecting deductions from observations. E. Comparison of results. F. Mean rate of increase of temperature with depth, and mean upward flow of heat. A. Instruments.—Under th is head, we have: 1. In stru- ments for observing temperature. 2. Subsidiary apparatus. 1. The thermometers which the committee have employed have been of two kinds—slow-action thermometers and maximum thermometers. The present pattern of slow-action thermometer consists of a thermometer having its bulb sur rounded by stearine or tallow, the whole instrument being hermetically sealed with a glass jacket, and had its origin in a conference between the secretary and Dr. Stapff in the St. Gothard Tunnel. Our present patterns of maximum thermometer are two —the Phillips, and the inverted Negretti—both being hermetically sealed in strong glass jackets to prevent the bulbs from receiving pressure when lowered to a great depth in water. Both instruments are used in a vertical position, and they register truly in spite of jolts in hauling up. References to Becquerel's thermo-electric method of observing underground temperature were made in three of the reports, and some laboratory experiments were subsequently carried out by the secretary, which led to the conclusion that the mei hod could not be relied on to yield sufficiently accurate results. It may be men! ioned that Becquerel's observation s are only carried to the depth of 100 feet, whereas we requ i re observations at the depth of 1,000 or 2,000 feet. 2. Under the head of subsidiary (that is non-thermometric) apparatus. plugs for preventing convection-current in a bore or well are referred to. Professor Lehour's umbrellalike plug, in its final form, appears to be very convenient, as it requires only one wire. It remains collapsed so long as the wire is taut, but opens out and plugs the hole when it becomes slack. B. Methods of Observation.—These have chiefly been of two kinds: 1. Observations in holes bored to the depth of a few feet in newly opened rock, either in the workings of a mine or a tun uel, or in a shaft during the sin king. The rock should not have been exposed for more tban a week when the hole is bored, and a day may be allowed t.o elapse for the heat generated by boring to escape before the thermometer is inserted. Very complete plugging is necessary to exclude the influence of the exteraai ai r. It is desirable to use about two feet of plugging, of wb ich the outer part should be made air-tigh t with plastic clay or greased rag. • After the lapse of a few days, the thermometer is to be drawn out by means of a string attached to the handle of its copper case, and the reading taken. The slow-action thermometer above described is employed for this purpose, and there is time to read it with sufficient deliberation before any appreciable change occurs in its indication. It is recommended.tbat the thermometer be then reinserted and plugged as before, and a second reading taken after' the lapse of a week. The majority of our successful observations have been made by this method. 2. Observations in deep bores of small dIAmeter. The first report contained a succesaful application of this metbod to a bore about 35) feet deep, near Glasgow, which gave very regular results in a series of observations at every sixtieth foot ajldeptfr; but in tlie majority of instances in 'which it has Hee been applied, there have been marked irregularities, due apparently to the influx of water from springs at particular points. One of the most valuable of our results was obtained by the application of the method to a bore 8113 feet deep, executed at tlie bottom of a coal mine 1,066 feet deep, giving a total depth of 1.929 feet. The bore in this case was dry at the time of its execution, though full of water at the time of the ohservation. It was in South Hetton Colliery, Durham. The instl'ument generally employed in the observations of this class was a maximum thermometer of either the Phillips or the inverted Negretti construction. The larger thfe diameter of the bore, the more uncertain does this mode of observation become. The South Hetton bore had a diameter of 2% inches. The Kentish-Town well, 1,000 feet deep, in which Mr. Symons' observations were made, had a diameter of 8 inches, and the well 660 meters deep at La Chapelle, in the north of Paris, had a diameter of 4% feet (V., VI., VII.). the temperatures in this last were proved to be largely affected by con vection, the water at the top being too warm, and that at the bottom not warm enough. The observations of Herr Dunker, in the bore at Sperenberg, near Berlin, with a depth of 3,390 feet, and a diameter of 12 inches, proved a si mil ar disturbance, amount- in g, at the top and bottom, to several degrees. As regards the bottom, the proof consisted in showing that when a thermometer at the bottom was protected by a tight plug from the influence of the water above, its indications were high er (= 6%° F.) than when this precaution was C. ^HIIk Affecting the Grneetnew of the Observations fe mijfBf theoretically incliirle questions as to the correct working of the in si ruments employed, and as to the personal reliability of observers; but the latter topic has iiot come into discussion, and the former has not arisen since our pre sent patterns of instrument came into use. The questions for discussion are thus confined to those wh ich relate to possible differences between tbe temperature of the point at which the thermometer was placed and the normal temperature at the same depth in its vici nity. 1. The heat generated by the action of the boring tool will vitiate the observation, if sufficient time is not allowed for its escape. A very full discussion of this subject in connection with the great artesian well at La Chapelle will be found in reports V., VI., and VII., clearly establishing the fact that the temperature at the bottom, both on the third and the sixth day after the cessation of boring operations, was 7^° F. higher than after the lapse of four months, though the water had been left to itself during th is interval. Further evidence sl!owing that the temperature in the lower part of a bore full of water may th us be raised several degrees is furnished by the sub- Wealden bore. 2. The generation of heat by local chemical action is well known to be a powerful disturbing cause whe!1 pyrites are present. The observers in the mines of Schemnitz say, '• Pyrites an d also decaying timber were avoided, as being known to generate heat.” The observations in the coal mines of Anzin show' a te mperut ure of 70%"° F. in shaft IV. (a very dry one) at the depth of 212 meters, or less than 70 feet. This must be about 15° F. above the normal temperature. In shaft II. th e observer mentions that there was, at a depth of 90 m., a seam of coal in which heat was generated by oxidation. At Talargoch lead mine, in Flintshire, the discrepancies between the temperatures at the six observing stations are suggestive of local chemical action. 3. Convection of heat has proved a very troublesome disturbing cause. As to convection of h eat by air in a shaft or well not filled with water, evidence will be found in the second report, both in the case of Mr. Hunter's observations in the shafts of two salt mines at Carrickfergus, hav i ng the depths of 570 and 770 feet respectively, and in the case of Mr. Symons' observations at Kentish Town, where the first 210 feet of the well are occupied witb air. At the depth of 150 feet the temperature was 521 in January, and 54'7 in July. Convection of heat by water in old shafts which have been allowed to become flooded is very manifest in some of the observations communicated by Mr. Burns in the second and fourth reports. In Allendale shaft (Northumberland), 300 feet deep, with about 150 feet of water, the temperature was practically the same at all depths in the water, and this was also the case in Breckon Hill shaft, where the observations extended from the depth of 42 feet to that of 350 feet. A similar state of th i ngs was found in a sh aft at Ashburton (Devon) hy Mr. Amery, who observed at every fiftieth foot of depth down to 350 feet. Convection by water in the great well at La Chapelle, 660 m. (2,165 feet) deep, and 1'35 m. (4 feet 5 inches) in diameter at the bottom, appears probable from the following comp ari sons: Very concordant observations (communicated by M. Wal- ferdin to Comptes Rendus for 1838) at three different wells in the Paris basin, of the respective depths of 263 m., 400 m., and 600 m., show by comparison with one another and with the constant temperature in the artificial caves under the Paris Observatory a rate of increase of 1* F. in 56 or 57 feet. These data would give, at the depth of lOO m., or 328 feet, a temperature of 57 , and at the depth of 660 m., or 2,165 feet, a temperature of 90°; whereas the temperatures actually observed at those depths in the well at La Chapelle in October, 1873, when the water had been undisturbed for a year and four months, were 59'5° and 76°. It thus appears pi'obable that the upper part of the well is warmed, and the lower part cooled, by convection. Further light may be expected to be thrown on this point when the well .reaches the springs, and the water spouts above the surface, as it does at the Puits de Grenelle. A letter received by the secretary in July, 1882, states that engineering difficulties have prevented any deepening of the well since the above observations, but that arrangements for this purpose have now been . made. More certain and precise information as to the effect of convection in deep bo res is furn ished bv the experiments of Herr Dunker at Sperenberg. The principal bore at Sperenberg has a depth of 4,052 Rhenish or 4,172 English feet, and is entirely in rock salt, witb the exception of the first 283 feet. Observations were flrst taken (with a maximum thermometer on the overflow principle) at numerous depths, from 100 feet to the bottom, and showed a fairly regular increase of temperature downward. The temperature at 700 feet was 16'Otl° R., and at 3,390 feet 341° R. Plugs we re then contrived which could be fixed tight in the bore at any depth with the thermometer between them, or could be fixed above the thermometer for observing at the bottom. Convection was thus preven ted, and a'difference of one or two degrees Reaumur was found in the temperatures at most of the depths; at 700 feet the temperature was now 17'06° R., and at 3,390 feet 36'15°. We have thus direct. evidence that convection had made the temperature at 3,390 feet 205° R., or 4'6° F. too low; and this, as Herr Dunker remarks, is an underestimate of the error, inasmuch as convection had been exerting its equalizing action for a long time, anii its effect could not be completely destroyed in the comparat ively short time that the plugs were ib position. Again, as regards the effect of convection on the upper part of the bore, the temperature 11'0° R. was observed at the depth of 100 feet in the principal bore when no plugs were em ployed, while a second bore only 100 feet deep in its immediate vicinity showed a temperature 9'0° R. at the bottom. This is direct evidence that the water near the top of the great bore had been warmed 2° R., or 44° F. by convection. . Suggestions for observations in filled-up bores will be found in the eleventh report, but they have not yet taken II practical shape. D. Questions Affeeting Dedwtiomsfrrom Observations.—l. In many instances, the observations of temperatu re have been confined to considerable depths, and in order to deduce the mean rate of increase from the surface downward it has been necessary to assume the mean temperature of the surface. To do this correctly is all the more difficult, because there seems to he a sensible difference between the mean temperalure of the surface and that of the air a few feet above it. Iu the third report some information on this point is given, based on observations of thermometers 22 inches deep at some of the stations of the Scottish Meteorological Society, and of thermometers 3 (French) feet deep at Greenwich aud at Edinburgh. These observations point to an excess of sur face temperature above air temperature, ranging from half a degree to nearly two degrees, and having an average value of about one degree. , Dr. Schwartz, Professor of Physics in the Imperial School of Mines at Schemnitz, in sending his observations made in th e mines at that place, remarks ou this point: "Observations in various localil ies show that in sandy soils the excess in question amounts, on the average, to about half a degree centigrade. In this locality the surface is a compact rock, which is high ly heated by the sun in summer, and is protected from radiation by a covering of snow in winter; and the conformation of the hills in the neighborhood is such as to give protection agai i:st the prevailing winds. Hence the excess is probably greater here than in most places, and may fairly be assumed to be double the above average." Some excellent observations of underground temperature at small deplhs were made at the Botanic Gardens, Regent's Park, London, for the six years 1871--76, along with observations of air temperature, and Jiave been reduced by Mr. Symons. They are at depths of- S, 6, 12. 24, and 48 inches beneath a surface of grass, and their joint mean derived from read ings at 9 A.M. and 9 P.M. for the six years if! 49 9, the mean for tbe 48-inch thermometer. being 50 05. The mean air temperature derived in the same way from the readings of the dry bulb t hermometer is 49'6, Hence it appears that the excess of soil above air is in this case about 0 4'. Quetelet's observations for three years at Brussels (p. 48 of his “ Memoire “) make the earth, at depths less than feet, col der than the air, and at greater depths warmer than the air. Caldecott's observations for three years at Trevandrum, in India, make the ground at the depth of 3 feet warmer th an the air by 5'7° F. Dr. Stapff, in his elaborate publications on the temperature of the St. Gothard tunnel, arrives at the conclusion that the mean temperature of the soil on the surface of the mountain above the tunnel is some degrees higher than that of the air. the excess increasing with the height of the surface and ranging from 2° or 3° C. near the ends of the tun nel to 5° or 6° in the neighborhood of the central ridge. 2. Connected with this is the question whether the mean annual temperature of the soil increases downward from the surface itself, or whether, as is sometimes asserted, the increase only begins where annual range ceases to be sensible —say at a depth of 50 or 60 feet. The general answer is obvious from the nature of conduc tion. Starting with the fact that temperature increases downward at depths where the annual range is insensible, it follow s that heat is traveling upward, because heat will always pass from a hotter to a colder stratum. This heat must make its way to the surface and escape there. But it could not make its way to the surface unless the mean temperature diminished in approaching the surface; for if two superposed layers had the same mean temperature, just as much he.lt would pass from the upper to the lower as from the lower to the upper, and there would not be that excess of upward flow which is uecessary to carry off the perennial supply from below. This reasoning is rigorously true if the conducti vity at n given depth be independent of the temperature, and be the same all the year round. By “ conductivity “ we are to understand the “ fiux of heat” divided by the “ temperature gradient,” where by the “flux of heat “is meant the quantity of heat which flows in one second across unit area at the depth considered, and by the “ temperature gradient” is meant the difference of temperature per foot of descent at the depth and time considered. Convection of heat bv the percolation of water is here to be regarded as included in con d uction. If the cond ucti vity as thus defined were the same all the ye ar round, the increase of me an temperature per foot of de pth would be i nd epe n den t of the ann ual range, and would be the same as if this range did not exist. . As a matter of fact, out of six stations at which first-class uiiderground thermometers have heen observed, five show an increase downward, and one a decrease. The following are tbe result s obtained for the depths of 3, 12, and 24 French feet: 3 feet. 12 feet. 24 feet.. Brussels, three years 51*85 53 69 53'71 Edinburgh (Craigleith) five years 45SS 45'92 4607 Edinburgh (Gardens) five years 46'13 46'''6 47'09 “ . (Observatory) seventeen years 46'27 4692 47'18 Trevandrum (India) three years, 85 71 86'12 Greenwich, fourteen years..... 50'92 50 61 5028 In calculating the mean temperature at 12 feet for Trevandrum, we have assumed the temperature of May, which is. wanting, to be the same as that of April. Omitting Trevandram, and taking the mean values at 3 and 24 French feet, we find an increase of 0'656 of a degree in 21 French feet, wbich is at the rate of 1° for 32 French or about 34 En glish feet. _ 3. Another question which it has sometimes been necessary to discuss is the influence which the form of the surface exerts on the rate of increase of temperature with depth. The surface itself is not in general isothermal, but its temperature is least where its elevation is greatest; the rate of decrease upward or increase downward being generally estimated at 1 ° F. for 300 feet. This is only about one-fifth of the average rate of increase downward in the substance of the earth itself beneath a level surface. If the two rate;: were the same, the isotherms in the interior of a mountnin would be horizontal, and the form of the surface would have no influence on the rate of increase of temperature with depth. The two extreme assumptions that the surface is an isotherm, and that the isotherms are horizontal, lie on opposite sides of the truth. The isotherms, where they meet the sides of the mountain, slope in the same direction as the sides of the mountain, but to II less degree. Probably the tangents of tbe two slopes are generally about as 3 to 4. Further, if we draw a vertical line cutting two isotherms, the lower one must have less slope than the upper, because the elevations and depressions are smoothed off as the depth increases. The practical inference is that the distance between the isotherms (in other words, the number of feet for 1° of increase) is greatest under mountain crests and ridges, and is least under bowl-shaped or trough-shaped hollows. The observations in the Mount Cenis tunnel, and the much more complete observations made by Dr, Stapff in the St. Gothard tunnel, fully bear out these predictions from theory. The discussion of the former occurs in the fourth report,p.15. As regards the St. Gothard tunnel , Dr. Stapff reports; “'The mean rate of increase downward in the whole length of the tunnel is 0'02068 of a degree C6fltigrade per meter of depth, measured from the surface directly over. This is 1° F. forSS feet. Where the Burface isa steep ridge, the increase is less rapid than this average; where the surface is a valley or plain, the increase is more rapid," © 1882 SCIENTIFIC AMERICAN, INC. 5812 4. The question whether' the rate of increase downward is,' upon the whole, the samn, at all depths, was raised by Prof. Mohr in his comments upou the Sperenberg observation!', and is discussed, so far Its these observations bear upon it, j in the ninth and eleventh reports. : Against the Sperenberg observations, which. upon the : whole, show a retardation of the rate of increase as we go ! deeper,may now be set tbe Dukinfield observations. begun by | Sir William Fairbairn and continued by Mr. Garside. Tak-1 irig Mr. Garside's observations, and assuming a surface temperature of 49” the increase in the first 1,987%, feet, is at the rate of 1 ° in 79 5 feet; in tbe next 420 feet it is at the rate of 1° in 70 feet; and in the last 283^ feet it is at the rate of 1” in 51%, feet. From a theoretical point of view, in places where there is no local generation of heat hy chemical action the case stands tbus: The flow of beat upward must be the same at all depths, and this flow is equal to the rate of increase downward multiplied by the conductivity, using the word “ cou.ductiv ity” (as above explained) in such a sense as to include convection. The rate of increase downward must, tlierefore, be the same at nil depths at which this conductivity is the same. This reasoning applies to superposed strata at the same place, and assumes them to be sufficiently regular in their arrangement to insure tbat tbe flow of beut shall be in parallel lines, not in converging or diverging lines. 5. If we have reason to believe that the flow of heat upward is nearly the same at all places, then tbe above reasoning can also be applied approximately to the comparison of one place with another—that Is to say, the rates of increase downward, in two masses of rock* at two different places, must be approximately in tbe inverse ratio of their conductivities. In tbe cooling of a heated s here of heterogeneous composition, the rates of flow wouldat first be very unequal through different parts of the surface, being most rapid through ,those portions of the substance which conducted best; but these portions would tbus be more rapidly drained of their bpat than the other portions, and tbus their rates of flow would fall off nlol'e rapidly than the rates of flow in the other portions. If the only differences in the material were differences of conductivity, we might on this account expect the outflow to he after a long time nearly the same at allparts of the surface. But when we come to consider differences of “t hermal capacity per unit volume,” it is clear that witb equal values of” diffusivity,” that is, of - conductivity divided by thermal capacity of unit volume” in two places, say in two adjacent sectors of the globe, there would be the same distribution of temperatures ill both, but not the same fiow of heat, this latter being greatest in the sector iti which the capacity and conductivity were greatest. . Wbere we find, as in Mr. Deacon's observations at Bootle, near Liverpool, and to a less marked degree in the observations of Sir William Fairbairn and Mr. Garside, near Man cbester, an exceptionally slow rate of increase. without exceptionally good conductivity, it is open to us to fall back on the explanation of excepticnally small thermal capacity per unit volume in the underlying region of tbe earth, perhaps at depths of from a few miles to a few hundred miles. 6. A question which was brought into consideration by Prof Hull, in connection with the great difference between the. rate of increase at Dukinfield and that at Rosebridge, is the effect of the dip of the strata upon the vertical conductional of heat. Laminattd rocks conduct heat much better along the planes of 1 lamination thiln at right angles to them. If fo denote the conductivity along, and ks the conductivity normal to the planes of lamination, and if these planes are inclined at •in angle 1/ to the horizon. the - number of feet per degree of increase downward corresponding to a given rate of outflow through the surface will be the same as if the flow were vertical with a vertical conductivity: ki sin' k C8. Prof: Herechel finds about 1'08 a” the ratio of the two principal conductivities ill Loch Rarinoch flagstone, and 1 “W5 as the ratio in Festiuiog slate. The dip of the strata at Dukinfield is stilted by Mr. Garside to lie 1")°, and we have siri-' 15°= 0-07, cos' 15°=0'93. If we assume k,=1-8k». as in the case of fiagstune, we find for' the effective vertical conductivity k. (0-09+0'98)=1 '02 k.., so that the number' of feet per degree would only be increased bv 2 per cent. It is not likely that, the two conducth'ites in the strata at Diikinfleld are so unequal as even in the case of flagstone, 110 tbat 2 per cent. is high estimate of the effect of their clip on tlie vertical rate of increase so far- as pure conduction is concerned. The effect of dip in promoting the percolation of water is a distinct consideration, but the workings of the Dukinfield mines are so dry that this action does not .seem to be important* E. We now proceed to a comparison of results. - The localities at which definite results have been obtained may thus be classified : 1 Metallic mines. 2. Coal mines. 3. Wells and wet 4. Tuunels. 1. Tlie mines tit Przibram iu Bohemia. witb a depth of 1,900 feet, are in very quartzose rock, and give a very slow rate of increase, viz., 1' F. in 135 feet. As all the shafts are in lofty hills, an allowance of may be made for convexity, leaving l' F. in 126 feet. Quartz is found by Prof. Herschel o The mines at Schemnitz in Hungary, with a depth of 1,368 feet, give an average r ate of 1” F. in 74 feet, the rock being a green hornblende-andesite (in German, Oriinstein-Trachyl), which is a compact, fine-grained, crystalline, more or less vitreous. rock. Prof. Lebour estimates its conductivity as heing probably nearly the same as that of Calton Hill trap- rock, whicb Prof. Herschel found to be about 0'0029. 2. The principal results from coal mines are as follows : The mines of the Societe Cocqueril at Seraing (Belgium), with a depth of 1,657 feet, give an average rate of 1 F. in 50 feet. The rock is coal shale. Prof. found for shale the low conductivity 0'0019. Tbe m:::es of Anzin, in the north of France, with a depth of 658 feet, gave in the deepest shaft an increase or 1° in 47 feet. Rosebridge Colliery, near Wigan, witb a depth of 2,445 feet, gave a mean rate of 1 in 54 feet. The four following are in the East Manchester coalfield : Astley Pit. Dukinfield, with a depth of 2,700 feet, gave a mean rate of 1° in 72 feet , Ashton Moss Colliery, with a depth of 2, 71 feet, gave 1° in 7"1. feet. ^Though the workings nl"t' dry, there is a large quantity of water In the superincumbent strata. Bredbury Colliery, with a dcplh ot' 1.020 feet, ga ve l' in 78'5 feet. ' Nook Pit, with a depth uf 1,030 feet, gave 1° iu 79 ft'et. South Hetlon Colliery, Durham, with a depth of 1,9211 feet, including n bore hole at bottom, gives very consistent observations at various depths, and tin average rate of I ° in 57'3 feet, Boldon Collierj-, between Newcast le and Sunderland, witb a depth of l',5l4 feet, and excellent conditions of observation, gives an average rate of 1 ° in 49 feel. Kingswood Colliery, near Bristol, with 11 depth of 1,769 feet, and remarkable consistency between observations tit various points, gives 1” in 68 feet. Prof. Phillips' observations in Monkwearmouth Colliery, published in Phil. Mag. for December, 1SJ4. sbowed a temperature of 71'2 in a hole bored in the floor of a recently exposed part at the depth of 1,584 feet The surface of the ground is 87 feet above high water, and the mean temperature of tbe air is assumed by Prof. Phillips to be 47'6. If, as usual, we .add l' to /let. the soil temperature, instead of assuming,. as Prof. Phillips does, thilt the temperature 100 feet deep is identical willi the nir temperature at the surface. we obtain a rale of increase of l' in 70 feet. 8. The following are the most trustworthy results from wells and borings: The Sperenbf'rg bore, near Berlin. in rock lIalt, with a depth' of 8,492 English feet, to the deepest reliable observation gave an average of 1 ° in 51'5 feet. This result is entitled to special weight, not only on account of the great depth, but also on account of the powerful means employed j to exclude convection. ! Rock salt, according to Prof. Herschef, has the very high conductivity 0'0118. Three artesian wells in the chalk of the Paris basin gave the following results: Feet. Rate, feet. St. Andre, depth of observation.. 830 l° in 56'4 Grenelle 1,812 1° in 56'9 Militnrv School 568 1° in 56-2 An artesian well at St. Petersburg, In the Lower Silurian strata, with a depth of 656 feet. /lave about 1 in 44 feet. A well sunk at Yakoutsk, in Siberia, to the depth of feet, disclosei I the fact that the ground was permanently frozen to this depth, and probably to tle depth of 700 feet. The rate of increase of temperatur'e was 1 ° in 52 feet. Of the English wells in which obsei'vations have been laken, the most important is that at Kentish Town, in which Mr. G. J. Symons, F.R.S., has taken observations to the depth of 1,100 feet. The temperatures at different depths form a smooth series, and have been confirmed by observations repeated at long intervals. The only question that can arise as to the accuracy uf the results is the possibility of their being affected by convection. The well IS 8 feet in diameter, with brickwork to the depth of 540 feet, and this part of it is traversed by an iron tube 8 incbes in diameter, which is continued to the depth I of more than 1,800 feet from the surface. The tube is • choked with mud to the depth of about 1,080 feet, so that: the deepest observations were taken under 20 feet of mud. I The temperature at 1,100 feet was 69'9", and hy combining , this with tlie surface temperature of 49'9° observed at the ' Botanic Gardens, Regent's Park, we obtain a rate of 1° in 55 feet. These data would give at 250 feet a calculated temperature of 54'5, whereas the temperature actually observed ; at this depth was 36-1, or 1'6° higber; tile temperature at j 300 feet and at 850 feet being also 56'1. This seems to indi- [ cnte convection, but it can be accounted for by convection in the 8-foot well which suri-ounds the tube. and does not imply convection currents within the tube. Convection cur-! rents are much more easily formed in water columns of large , diameter than in small ones, and the 20 fe'et of mud at tbe bottom give some security against convection tit the deepest point of observation. It'is important to remark that the in- j crease from 1,050 to 1,100 feet is rather less tlan the average ' instead of being decidedly greater, as it would be if thei'c i were convection above. but not in the mud. Tlie rate of l° ! ii 55 feet may therefore be adopted as correct. The strata Consist of Tertiary strata, chalk (586 feet thick), upper greensand, and gmilt. The Kentish Town temperature tit the rleptb of 400 feet (58 °) is confirmed by observations ID Mr. Sic^ s well at Cliis- j wick, which 395 feet deep, and hal! it temperature varying , from 58° to 57 5 ; The Bootle well, belonging to the Liverpool Water-works, | is 1,302 feet deep, and tlie observations were taken in it dur. i convection might have been suspected but for the circumstance tlat there was a gradual upward flow of water from the bottom, which escaped from the upper part of the well by percolation to an underground reservoir neiir at hand. This would check the tendency to downflow of colder water from the top; and as the observations of temperature were always made at the bottom, they would thus be protected against convective disturbance. The temperature at 226 feet was 52', at 750 feet 56° , at 1,302 feet 59 giving by comparison of the first and last of these a mean rate of 1 in 154 feet. The circumstance that tbe boriug ceased for six weeks at the depth of 1,00 feet, and the temperature fell during this interval from 1)8-1 ° to 57-0°, would seem to indicate an elevation of 1 ° due to tlie heat generated “y the boring tool. An assumed surface temperature of 49 ° (only 0'9 ° lower than that of tne Botanic Gardens a o 1 feet.a rate ofl°in 125%, fret, and by comparison with 59°, at 1,802 feet, a rate of V in 180 feet, which last may be adopted as the best determination. Tlie rock consists of the pebble beds of the Bunter or Lower Trill8, and the boring was executed at the rate of nearly 100 feet per month. The boring at Swinderby, near Searle (Lincoln), in search of coal, was carried to a depih of 2,000 feet, with a diameter at the lower part of only 31, inches—a circumstance favorable to accuracy, botb as impeding convectJon and as promoting the rapid escape of the heat of boring. The temperature at tbe bottom was 79°, the water having been undisturbed for a mouth, ami tb.s, by comparison with an assumed surface temperature, of 50", g. ves II rate of 1° iii 69 feet. . . The rocks are Lower Lias, New Red Marl (569 feet thick), New Red Sandstone (790 feet thick), Red Marl, and earthy Limestone. The following results have been obtained from shallow borings. The first three were made under Sir William Thomson's direct'on, with a thermometer which could be read by estimation to hundredths of a degree: Blytliswood liore, near Glasgow, witb a depth of 347 feet, gave a very regular increase of 1° in 50 feet. Kirkland Neuk bore, in the immediate vicinity of the above, gave consistent observations at different seasons of the year from 180 feet to the bottom (354 feet), the rate being 1° in 53 feet. This bore passed through coal wbich had been “ very much burned or charred." South Balgrav hore, near Glasgow, and north of the Clyde, with an available depth of 525 feet, gave, by com paring the temperature at the bottom with that at, 60 feet, a rate of 1* in 41 feet. . Shale extends continuously from 890 to 450 feet from the surface. and the increase in these 60 feet of shale wes 2'02', wbicb is at, tbe rate of l° in 80 feet. This rapid increase agrees with the fact that shale lias very low conductivity, averaging 0'0019 in Prof. Herschel's experiments. The only small bore remaining to be mentioned is that at llanegaon, in India, wbicb had 310 feet available, and gave. hy comparing the temperature at this depth with tbat at 60 feet, a rate of 1° in 68 feet. The rocks consist of fine softisll sandstones and hard silty clays, the dip being 10". - 4. Tiinnels.—The Mont Cenis tunnel, wliicll is about seven miles long. is at a depth of exactly .a mile (5,280 feet) beneath , lbe crest of Mont Frejus overhead. This was the warmest part of the tunnel, and had a temperature of 85'1° F. Tlie mean air temperature at the crest overhead was calculated by the engineer of the tunnel, M. Giordano. by inlerpolaling. between the known temperature of the liill of Ban Theodule and that of the city of Turin, the former' being 480 meters higher, and the latter 2,650 meters lower, than tbe point in question. It is thus calculated to be — 2'6° C. or 27'8° F. lf, according to our usual rule, we assume the ground to be 1 ° warmer than the air, we have 28'3° to compare with 85'1°. This gives a rate of 1° in 98 feet; but, inasmuch as the con; vexity of the surface increases the distance between the isotherms, a correction will be necessary before we can fairly compare this result with rates under' level ground. As a rougb estimate we may take t of 93, and adopt 1 < in 79 feet as lhe corrected result. ” The rocks on which the observations have been made are absolutely tbe same, geologically and ntherw isej from the entrance to the tunnel, on the Italian side. for a distance of nearly 10,00 yards. They are not faulted to any extenl, though higbly inclined, contorted, and subjected to slight, slips and slides. They consist, to a very large extent indeed, of silicates, cbiefiy of alumina, and tbe small quantity of lime they contain is a crystalline carbonate.- , The St. Gothard tunnel, which has a length of about nine miles, has been subjected to much more minute observation, a skilled geologist, Dr. Stapff, having, under government direction, devoted his whole time to investigating its geology and physics. He not only observed tbe temperature of tlie rock in tbe tunnel at very numerous points, but also determined, by observations of springs, the mean temperatures of the surface of the mountain at various points, and compared these with an empirical formula for air temperature deduced from the known mean temperatures of the air at. Gilschenen, Andermatt, Airolo, and the Hospice (If St. Bernard. He infers from his comparisons a considerable excess of soil above air temperature, increasing from 2° C. at the ends of tbe tunnel to 6° C. at the crest of the mountain over tbe center of the tunnel. The highest temperature of the rocks in the tunnel was at this central part, and was about 30'6' C. or 87° F. The soil temperature at the crest above it was about—0'6° C. or31° F., giving a difference of 56° F. The height of the crest above sea- level was about 2,850 m., and tbat of the tunnel at this part 1,150 m., giving a difference of 1,700 m. or 5,578 feet. The rate of increase here is, therefore, about 1° F. in 100 feci: and if we apply the same correction for convexity as in the case of the Mont Cenis tunnel, this will be reduced to about 1° F. in 87 feet as the equivalent rate uuder a level surface. From combining his observations in all parts of the tunnel through the medium of empirical formul®, Dr. Stapff deduces an average rate of 1 ° F\ for every 88 feet measured from the surface directly overhead. Where the surface is a steep ridge, the increase was ltls rapid than this average; where the surface was a valley or plain, the increase was more rapid. As this average merely applies to the ae- tual temperatures, the application of a correction for th* general convexity of the surface would give a more rapid rate. If we bring the isotherms nearer by one part in 15. wh!ch seems a fair' assumption, we IIball obtain a rate of 1 F. iii H2 feet. Collecting together all tbe results which appear reliable, and arranging them manly in the order of their i-ates of increase, but also willi some reference to locality, we have tbe following list: Depth, Feet feet. for 1° F. Bootle waterworks (Liverpool) 1,392 130 Przibram mines (Bohem^) 1,000 126 St. Gothard tunnel 5,578 82 Mont Cerris tunnel 5,280 79 TalargCl!h lead mine (Flint) 1,041 80 Nook Pit, Coll.ery 1,050 79 Bredbury “ East ... .1,020 78%, Ashton Moss “ ^-Manchester ^ 2,790 77 Denton '' coalfield 1,317 77 Astley Pit, Dukinfield. J 2,700 -32 Schemnitz mines (Hungary) 1,868 74 Bearle boring (Lincoln). ..." 2,000 69 Manegaon boring (India) 3lO 68 Pontypridd colliery (S. Wales) 855 76 Kingswood “ (Bristol) 1,769 68 Radstock “ (Bath) 620 62 Paris artesian well, Grenelle 1,312 57 ti ” '' “ Military School 568 06 London “ “ KeiitisliTown 1,100 55 Rosebridge colliery (Wigan! 2,441) 54 Yakoutsk, frozen ground (S!beria) 540 52 Sperenberg, boring iii salt (Berlin) 3,4112 51%, Seraing collieries (Belginm) 1,657 50 Monkwearmouth collieries (Durham) 1,1)84 70 ' South Hetton " ” 1,929 57^ Boldon '' ” 1.514 49 “ Whitehaven ” (Cumberland) 1,250 45 Kirkland Neuk hore (Glasgow) 854 58 Blythswood “ “ 347 50 South Balgrav “ “ 525 41 ' Anzin coliienes (north of France) 658 4'2' St. Petersburg, well (Russia) 656 44 Carrickfergus, shaft of salt mine (Ireland)... 770 4:n | “ “ ..• 570 40 Slitt mine, Weardale (Northumberland) 660 34' The depth stated iS in each case that of the dee observation that has been utilized. ; F. In deducing a mean from, fJttfle very various results, it is better to operate, not upon the number of feet per degree. but npon its reciprocal—the increase of temperature per foot. Assigning to the results in lhe foregoing list weights proportional to the depths, the meanincrease of temperature per foot is found to be 0 01563, or about ^ of a degree per foot-that is, 1° F. in 64 feet. It would be more just to assign greater weight to those single results which represent a large district or an extensive group of mines, especially where the data are knowIl ttl hi! very accurate. Doubling the weights above assigned to Przibram, St. Gothard, Mont Cents, Schemnitz, Kentisfi Town. Rosebrid.se, and Seraing, and quadrupling that a8- signed to Sperenberg, no material difference is made in the result. The mean still comes out 1° F. in 64 feet, or more exactly, 0'01566 of a degree per foot. This is a slower rate than has been generally assumed, but it has been fairly deduced from the evidence contained in thc committee's reports; and there is no reason to throw doubt on the results in the upper portion of the above list more than on those in its lower portion. Any error that can reasonably l>e attributed to the data used iu the calculations foi' the St. Gothard tunnel and for the numerous deep mines of the East Manchester coalfield', will have only a trifling effect on the rates of increase assigned to these localities. To obtain an approximation to the rate at which heat escapes annually from the earth, we will first reduce the above rate of increase 001566 to centigrade degrees per centimeter of depth. Fell' this purpose we must multiply by 0'0182, giving 0000285. To calculate the rate of escape of heat, this must be multiplied by the conductivity. The most certain determinations vet made of the conductivity of a portion of the earth's suhstance are those deduced by Sir William Thomson by an indirect method, involving observations of underground thermometers at three stations at Edinburgh, combined with laboratory measurement of the specific heats and densities of the rccks in which the thermometers were planted. The specific heats were determined hy Regnault, and the densities by Forbes. Specific heats and densities can be determined with great accuracy in the laboratory, but the direct determination of conductivity in Ihe laboratory is exceedingly difficult, it being almost “impossible to avoid sources of error which make the conductivity appear less than it .really is. Prof. Herschel, in conjunction with a committee of the British Association, has made a very extensive and valuable series of direct measurements of the conductivities of a great variety of rocks, and has given additional certainty to his results by selecting as two of the subjects of his experiments the Calton Hill trap and Craigleith sandstone, to which Sir William Thomson's determinations apply. From combining Prof. Herschel's determinations with those of Sir Wm. Thomson, 0'0U58 is adopted as the mean conductivity of the outer crust of the earth, which, being multiplied by the mean rate of increase, 0'^W285, gives 16,330X10-10 as the flow of heat in a second across a sqilf,re centimeter. Multiplying by the number of seconds in a year, which is approximately 31% millions, we have 1,633 X315X10-* =41'4. This, then, is our estimate of the average number of gramme-degrees of heat that escape annually through- each square centimeter of a horizontal section of the earth's substance.

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